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%I #16 Sep 06 2014 11:03:23
%S 20,64,336,1160,5896,24652,117628,531136,2559552,12142320,59416808,
%T 290915560,1449601452,7269071976,36877764000,188484835300,
%U 972003964976,5049059855636,26423287218612,139205945578944
%N Cogrowth sequence for Richard Thompson's group F with the standard generating set x_0, x_1.
%C a(n) is the number of reduced words in {x_0,x_0^{-1},x_1,x_1^{-1}}^* of length 2*n equal to the identity in F.
%H Murray Elder, <a href="/A246877/b246877.txt">Table of n, a(n) for n = 5..23</a>
%H M. Elder, A. Rechnitzer, T. Wong, <a href="http://arxiv.org/abs/1108.1596">On the cogrowth of Thompson's group F</a>, Groups, Complexity, Cryptology 4(2) (2012), 301-320.
%H S. Haagerup, U. Haagerup, M. Ramirez-Solano, <a href="http://arxiv.org/abs/1409.1486">A computational approach to the Thompson group F</a>, Arxiv 2014
%e The length of the shortest relation in the group presentation is 10, there are 20 distinct cyclic permutations of this word and its inverse, and each one is a reduced trivial word of length 2*5, so a(5)=20.
%K nonn,hard
%O 5,1
%A _Murray Elder_, Sep 06 2014
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